Coin Exchange Problem (max combinations)

Coin_Exchange.js

//************************************************************************//
// Coin Exchange Problem                                                  //
// most combinations to exchange n cents with m coins {C1, C2, ... , Cm}  //
// by Ron Marks                                                           //
//      ex input:  5 3                                                    //  
//                 1 2 3                                                  //
//      output:    4                                                      //
//      Explanation: 5 cents, 3 coins (1, 2, 3)                           //
//          { (1,1,1,1,1), (1,1,1,2), (1,2,2), (1,1,3), (2,3) }           //
//      Final Array:                                                      //
//          [ [ 1, 1, 1, 1 ],                                             //
//            [ 0, 1, 1, 1 ],                                             //
//            [ 0, 1, 2, 2 ],                                             //
//            [ 0, 1, 2, 3 ],                                             //
//            [ 0, 1, 3, 4 ],                                             //
//            [ 0, 1, 3, 5 ] ]                                            //
//************************************************************************//

function processData(input) {
    var lines = input.split("\n");
    var n = parseInt(lines[0].split(" ")[0]);      // n cents
    var m = parseInt(lines[0].split(" ")[1]);      // m coins
    var coins = lines[1].split(" ").map(Number);   // array of coin values
    
    var arr = new Array(n+1);                      // Create 2d array size n+1 x m+1
    for (var i=0; i<n+1; i++){
        arr[i] = new Array(m+1);
    }
    
    for (var i=0; i<n+1; i++){                     // arrays top row = 0
        arr[i][0] = 0;
    }
    for (var i=0; i<m+1; i++){                     // arrays first column = 1
        arr[0][i] = 1;
    }
    
    for (var j=1; j<m+1; j++){
        for (var i=1; i<n+1; i++){
            if (coins[j-1] > i){                   // if coin[j-1] is greater than i, take value above
                arr[i][j] = arr[i][j-1];
            } else {                               // else take values above, plus value to the left coins[j-1] places
                arr[i][j] = arr[i][j-1] + arr[i-coins[j-1]][j];
            }
        }
    }
    console.log(arr[n][m]);                        // Final answer
}